Unit Conversions Tutor

Converting units in either metric or English units (or combos) are essential to chemistry, physics, biology, or any science. And it's fairly easy to do as long as you can multiply, divide, add and subtract.

Basic Unit Conversion:

We will start with a very simple unit conversion, which should be very easy for you to do. We will convert 48.3 inches into feet. Before we do this we need to know how many of one type of unit equals another. Well, 12 inches = 1 foot and we will use this for our conversion factor. We start by writing the number we want to convert like so...

48.3 in

Next we set up the conversion factor:

Now we need to decide where to put the 12 inches and where to put the feet. We need the inches to divide out, so inches will go on the bottom.In fact you should put the units in BEFORE you put in the numbers!

then put in the numbers and calculate:

Metric to Metric Conversions:

When converting metric units you will need to know the metric prefixes and many teachers ask that you memorize them! I think memorization is best done through practice, so the more practice problems you do with unit conversion, the better you will become at it.

yotta- (Y-)

1024

1 septillion

zetta- (Z-)

1021

1 sextillion

exa- (E-)

1018

1 quintillion

peta- (P-)

1015

1 quadrillion

tera- (T-)

1012

1 trillion

giga- (G-)

109

1 billion

mega- (M-)

106

1 million

kilo- (k-)

103

1 thousand

hecto- (h-)

102

1 hundred

deka or deca- (da-)

10

1 ten

deci- (d-)

10-1

1 tenth

centi- (c-)

10-2

1 hundredth

milli- (m-)

10-3

1 thousandth

micro- (µ-)

10-6

1 millionth

nano- (n-)

10-9

1 billionth

pico- (p-)

10-12

1 trillionth

femto- (f-)

10-15

1 quadrillionth

atto- (a-)

10-18

1 quintillionth

zepto- (z-)

10-21

1 sextillionth

yocto- (y-)

10-24

1 septillionth

In all honesty, many of these are not necessary to memorize. The most important ones in chemistry are nano, milli, centi, deci, kilo, and mega

.
Lets try a quick conversion, we'll convert 0.0348 km into cm. There are two ways to do this:

Method 1:
You can first convert kilometers (km) into meters (m) and then convert meters (m) into centimeters (cm) like so...
Note that the number in red corresponds to the unit on the other side of the divistion line.

Method 2:
You can do the conversion directly. Many teachers don't like this second method, but I like it because it's a little faster.
Note that the colored number corresponds to the same color unit on the opposite side of the division line.

It is important to note that when converting from metric to English units you DO NOT use the number that goes with the metric prefix. For example, one inch is exactly 2.54 cm, so the conversion factor is simple (1 in / 2.54 cm). You would NOT write (0.01 in / 2.54 cm). THIS IS WRONG!

At this point you should try some exercises.
(1) Convert 3.84 miles to feet.
(2) Convert 67.2 inches to centimeters.
(3) Convert 3.8x105meters to kilometers.
(4) Convert 4.82 liters (L) to milliliters (mL).

I'm sure there are many more problems in your chemistry book and you should work as many of those as possible and check your answers!
Answers to problems above: (1) 2.03x104ft, (2) 171 cm, (3) 3.8x102, (4) 4.82x103 mL.

Unit Conversions with "Derived" Units:

A "derived unit" is essentially other units muiltiplied or divided.
For example m3 is meters cubed (meters to the power of 3), which measures volume.
And density often has units of g/mL (grams divided by mL).

But suppose we want to convert from 13.9 lb/ft3 (mass-pounds per cubic foot) to units of oz/in3 (mass-ounces per cubic inch). This is a bit difficult, especially if we don't have the conversion from cubic feet to cubic inches on hand. Here is the way we do it:

You'll note that although we don't know how many cubic inches are in a cubic foot, this is very easy to calculate; see the exponent of 3!
(1 ft)3 = (12 in)3 = 1728 in3. Although this isn't necessary because we can just calculate it directly. And finally:

Here are some sample problems:
(5) Convert $2.93/gal into Euros/Liter. (You will need to look up the conversion rate from dollars to Euros because it changes every day.)
(6) Convert the density of gold, 19.32 g/mL, into kg/m3.
(7) Convert Usain Bolt's top speed of about 42 mi/h into m/s.
(8) Convert $25/h into cents/s.
Answers: (5) approximately € 0.57/L, (6) 19320 kg/m3, (7) 19 m/s, (8) 0.6944 ¢/s.